The Relation of Aperture and Power. By Prof. Abbe. 463 



arc, the necessary amplification, N, for a distance of 250 mm. or 

 10 inches (1' being = 1 : 3438) is 



250 v 



N = 



3438 5 ' 



/\\ 



and substituting for 8 its equivalent in terms of the aperture ( — ) 

 we obtain the general formula : — 



250 lav 

 ~ 3438 ' ~a7 ' 



or, if X, is taken = ■ 00055, 



N = 264-5 a v. 



By introducing into this formula v = 2' and v = 4' respectively 

 we obtain the figures of useful amplification for a series of different 

 apertures as shown in Table I. — useful, that is, so far as delineating 

 power is concerned, putting aside for the moment any question 

 as to the illumination of the object, which, as explained hereafter, 

 allows of somewhat greater apertures. 



Table I. 



